Finite Group DatabasebetaFinite Group Databasebeta| order | 864 |
| automorphism | ? |
| homology | Abelianization (H1) = C2×C8 · Schur multiplier (H2) = C1 |
No aliases for this group.
| Fitting | C16×C27 ⋊ C2 |
| Sylow | C27 ⋊ M32 |
52 conjugacy classes of subgroups.
| minimal degree | μ(G) = 43 |
| transitive degree | μt(G) = 432 |
Polycyclic presentation:
2^5,3^3|b^2=c,c^2=d,d^2=e,f^3=g,g^3=h,b^a=be,f^a=f^2g^2h^2,g^a=g^2h^2,h^a=h^2228 conjugacy classes — view the full character table.
| maximal subgroup of | C2×#11720039, #13134407, M32×D27, … |
| maximal normal subgroup of | C2×#11720039, #13134407, M32×D27, … |
| maximal quotient of | Dic27⋊C16, #13133999, (C2×D27)⋊C16, … |
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(864, 6);